# odd distance

## Coloring the Odd Distance Graph ★★★

Author(s): Rosenfeld

The \emph{Odd Distance Graph}, denoted ${\mathcal O}$, is the graph with vertex set ${\mathbb R}^2$ and two points adjacent if the distance between them is an odd integer.

\begin{question} Is $\chi({\mathcal O}) = \infty$? \end{question}

Keywords: coloring; geometric graph; odd distance